2 years ago

Fool's problem of the day,
If \( f(x,y) \) is a function that gives the remainder when \(x\) divided by \( y \). Prove that the value of \( f(124^{24},99) - f(173^{24},99) =0\).
Problems credits: IMS india.

How about... Notice that this function is the same as the mod function We want to show \[124^{24}\equiv174^{24}\pmod{99}\]Reduce, and get that this is equivalent to asking \[25^{24}\equiv74^{24}\pmod{99}\]Since \(74\equiv-25\pmod{99}\), we can simplify to \[25^{24}\overset{?}\equiv(-25)^{24}\pmod{99}\]Since we have an even exponent, this is clearly true.
This is basically the same thing asnaseer did.